2203.08298
MODELING OF ASYMPTOTICALLY PERIODIC OUTBREAKS: A LONG-TERM SIRW2 DESCRIPTION OF COVID-19?
Alex Viguerie, Margherita Carletti, Alessandro Veneziani, Guido Silvestri
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Note/Short/Other
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper defines the SIRW2 ODE system and numerically exhibits wave-like behavior with time-independent parameters, but explicitly leaves rigorous existence/stability and bifurcation analyses for future work. The candidate model solution, by contrast, gives a sound Hopf-bifurcation-plus-perturbation construction: decouple to an SIRWS-with-boosting block known to undergo a generic Hopf, ensure the other block is strongly stable, and re-introduce small couplings so a hyperbolic limit cycle persists in the 8D living-compartment subsystem; m is monotone and not part of the periodic orbit. The argument is standard and, given the model structure, appears correct.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} note/short/other
\textbf{Justification:}
A clear and plausible modeling framework is proposed, and simulations suggest intrinsic periodicity with constant parameters. However, the central scientific claim (presence of limit cycles intrinsic to SIRW2) is not supported by a rigorous analysis. Given the importance of periodic behavior to the paper's message, at least a local bifurcation result (e.g., Hopf) or well-stated theorems with assumptions are needed for publication beyond a brief communication.